IPMAT Indore (MCQ) PYQs

If $f(1) = 1$ and $f(n) = 3n - f(n - 1)$ for all integers $n > 1$ , then the value of $f(2023)$ is

Let $f$ and $g$ be two functions defined by $f(x) = |x + |x||$ and $g(x) = \frac{1}{x}$ for $x \neq 0$. If $f(a) + g(f(a)) = \frac{13}{6}$ for some real $a$, then the maximum possible value of$f(g(a))$ is:

A real-valued function $f$ satisfies the relation $f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y$, for all real numbers $x$ and $y$, then the value of $f(8)$ is